# On Constructing Resolutions Over the Polynomial Algebra

## Leif Johansson, Larry Lambe and Emil Sköldberg

Let \$k\$ be a field, and \$A\$ be a polynomial algebra over \$k\$. Let \$I\subseteq A\$ be an ideal. We present a novel method for computing resolutions of \$A/I\$ over \$A\$. The method is a synthesis of Gr\"obner basis techniques and homological perturbation theory. The examples in this paper were computed using computer algebra.

Homology, Homotopy and Applications, Vol. 4(2), 2002, pp. 315-336

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